Narrow Results

Using the colored Kauffman skein relation, we study the highest and lowest $4n$ coefficients of the $n\mathrm{\text{th}}$ unreduced colored Jones polynomial of alternating links. This gives a natural extension of a result by Kauffman in regard with the Jones polynomial of alternating links and its highest and lowest coefficients. We also use our techniques to give a new and natural proof for the existence of the tail of the colored Jones polynomial for alternating links.